Kuramoto Extended: Heterogeneous Oscillators From Intracellular Collectives to Organismic Coherence

This paper extends the classical Kuramoto model of coupled oscillators to systems composed of heterogeneous components---oscillators that differ fundamentally in their intrinsic frequencies, internal dynamics, and mutual couplings. We take the neuronas a paradigmatic toy model, treating its internal components (mitochondria, ion channels, ribosomes, lysosomes) as a collective of diverse oscillators whose synchronisation produces the characteristic 40\,Hz gamma rhythm as an emergent property. This framework provides a mechanistic bridge between subcellular dynamics and multilevel coherence, showing how perturbations at the organelle level propagate across scales to produce the network-wide collapse observed in neurodegeneration. We embed this extended Kuramoto model within a unified conceptual framework---topological, oscillatory, and evolutionary---that integrates tools from Gradient Indeterminacy (I-G), the Drain Vortex Principle, and the Underlying Properties Hypothesis (UPH). We derive falsifiable predictions regarding distinct spectral signatures of organelle-specific insults and propose connectionsto personalised coherence monitoring via the Personal Coherence Baseline (PCB) magnitude.